Inverse estimation of front surface temperature of a locally heated plate with temperature-dependent conductivity via Kirchhoff transformation

IF 5 2区工程技术 Q1 ENGINEERING, MECHANICAL International Journal of Thermal Sciences Pub Date : 2013-07-01 Epub Date: 2013-04-02 DOI:10.1016/j.ijthermalsci.2013.02.004

Nazia Afrin, Z.C. Feng, Yuwen Zhang, J.K. Chen

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引用次数: 17

Abstract

In this paper, by Kirchhoff transformation of the temperature variable, the temperature dependence of thermal conductivity is eliminated, thereby simplifying the 3-dimensional heat conduction equation. Through Hadamard Factorization Theorem, transfer function relating the front and back surface temperature as infinite product of polynomial is established. The inverse Laplace transform of the polynomial provide the relationship for every mode in the time domain. The front surface temperature is revealed through iterative time domain operations from the data on the back surface. Seven points for smoothing and third order polynomial in derivative calculation were used in Savitzky–Golay (S–G) method. The comparison between direct solution, Conjugate Gradient Method (CGM) and DCT/Laplace transform solutions are given. Root Mean Square (RMS) of the errors at different time steps for DCT/Laplace solution and CGM method are also presented.

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利用基尔霍夫变换反演电导率随温度变化的局部加热板的前表面温度

本文通过对温度变量进行Kirchhoff变换，消除了导热系数对温度的依赖，从而简化了三维热传导方程。利用Hadamard分解定理，建立了前后表面温度作为多项式无穷积的传递函数。多项式的拉普拉斯逆变换给出了时域内各模态的关系。根据后表面的数据，通过迭代时域运算得到前表面的温度。Savitzky-Golay (S-G)方法采用7个平滑点和导数计算中的三阶多项式。给出了直接解、共轭梯度法(CGM)和DCT/拉普拉斯变换解的比较。给出了DCT/拉普拉斯解和CGM方法在不同时间步长的误差均方根(RMS)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Thermal Sciences 工程技术-工程：机械

CiteScore

8.10

自引率

11.10%

发文量

531

审稿时长

55 days

期刊介绍： The International Journal of Thermal Sciences is a journal devoted to the publication of fundamental studies on the physics of transfer processes in general, with an emphasis on thermal aspects and also applied research on various processes, energy systems and the environment. Articles are published in English and French, and are subject to peer review. The fundamental subjects considered within the scope of the journal are: * Heat and relevant mass transfer at all scales (nano, micro and macro) and in all types of material (heterogeneous, composites, biological,...) and fluid flow * Forced, natural or mixed convection in reactive or non-reactive media * Single or multi–phase fluid flow with or without phase change * Near–and far–field radiative heat transfer * Combined modes of heat transfer in complex systems (for example, plasmas, biological, geological,...) * Multiscale modelling The applied research topics include: * Heat exchangers, heat pipes, cooling processes * Transport phenomena taking place in industrial processes (chemical, food and agricultural, metallurgical, space and aeronautical, automobile industries) * Nano–and micro–technology for energy, space, biosystems and devices * Heat transport analysis in advanced systems * Impact of energy–related processes on environment, and emerging energy systems The study of thermophysical properties of materials and fluids, thermal measurement techniques, inverse methods, and the developments of experimental methods are within the scope of the International Journal of Thermal Sciences which also covers the modelling, and numerical methods applied to thermal transfer.